I ended up "borrowing" some BA miles from my brother (after all, I did tell hime about the Chase 100K offer

and booked
SFO-LIM(stopover)-SCL-IPC, IPC-SCL(stopover)-LIM-SFO
in business for 80K each. I'm glad with the value I got from the BA miles. Now I'm trying to figure out whether to use AA miles for inter-Peru flights or pay out of pocket.